The numerical formulation used to simulate the flow in injection molding has been presented. Velocity profile was calculated for three different fiber-polymer matrices using power law model. The simulation results support the fact that the viscosity of any fiber-polymer matrix increases as the consistency index (K) increases. That means , fibers with small consistency index influence the power law parameters the least. Therefore, it can be concluded that the velocity of such composites is larger compared to those with large consistency index for the same geometry and boundary conditions. The effect of short fibers, suspended in a non - Newtonian fluid, on the total stress of the melt was numerically analysed for simple shear flow. The constitutive equation includes additional term which represents the contribution of the fiber to the total shear stress. The theory and numerical methods used to simulate the fiber orientation in film-gated strip was also presented. The fiber orientation equation is solved using second order tensor method to represent the important statistics of the distributionfunction. The fibers tend to align perfectly to the flow direction at the mold walls due to formation of shear layer near the mold wall. However, since there is little shearing at the midplane, the orientation component a 11 is not changed significantly
In this paper we implemented the fibre segment orientation estimation scheme presented by Eberhardt and Clarke(Eberhardt & Clarke, 2002). This approach estimates fibre segment orientation using a brute force search of the spherical neighbourhood around each voxel. The algorithm performs a linear search in and of the spatial domain for the most probable orientation vector and computes a discrete approximation of the local orientation vector. Additionally, the algorithm is bounded by the selection of the step size in and as well as the length of l. The number of additions, multiplications and trigonometric function calls per voxel vary and trigonometric function calls can be eliminated by pre-computing angles. Therefore, every vector must be checked and compared to the current maximum intensity vector peak and this strategy offers no method of early termination. In addition to the slow speed of searching the spatial domain, the brute force method requires additional memory to compute the orientation vectors even with a slice-by-slice strategy. Additional slices must be streamed from disc in the neighbourhood of L to compute the orientation vectors. This requires more disc accesses, which is slow and the number of disc accesses varies with number of processors. Additional memory is required for computing the most probable orientation when there are multiple same maximum peak intensity values. The existing algorithm for fibre segment detection followed in this particular study is not scalable for larger data sets.
The A-fod cost function (Eqs. (3) and (5)) has a number of hyper- parameters that we need to set for the optimisation. These include the regularization parameter λ and the number of iterations. We used a k-fold cross-validation to ﬁ nd the optimal λ . Thirty thousand random white matter voxels from an HCP dMRI dataset and 61 candidate values for λ, logarithmically spanning the interval between 0.01 and 10, were considered. The signal in each of these voxels was divided into k parti- tions of n signal values and the values from k-1 sets were used to ﬁt the proposed model. To test the goodness of ﬁt on the k-th partition we computed the mean squared error (MSE) between the predicted and the measured signal. The λ parameter that was minimizing the MSE in every voxel was selected. This operation was repeated 61 k times by considering a different signal partition at each iteration. More specif- ically, we set k to 10, for a total of n ¼ 9 unique samples for each partition. We found that the optimal regularization parameter was λ ¼ 0.1 (this was the mode of the distribution of optimal λ across all voxels).
This thesis introduces a new approach to analysing spatial point data clustered along or around a system of curves or fibres with additional background noise. Such data arise in catalogues of galaxy locations, recorded locations of earthquakes, aerial images of minefields, and pore patterns on fingerprints. Finding the underlying curvilinear structure of these point-pattern data sets may not only facilitate a better understanding of how they arise but also aid reconstruction of missing data. We base the space of fibres on the set of integral lines of an orientation field. Using an empirical Bayes approach, we estimate the field of orientations from anisotropic features of the data. The orientation field estimation draws on ideas from tensor field theory (an area recently motivated by the study of magnetic resonance imaging scans), using symmetric positive-definite matrices to estimate local anisotropies in the point pattern through the tensor method. We also propose a new measure of anisotropy, the modified square Fractional Anisotropy, whose statistical properties are estimated for tensors calculated via the tensor method.
One of the best features of this method is benefiting from orthodox orientationdistribution functions to have a relatively impeccable anticipation of WPC mechanical property. There are so many functions which may fulfill conditions like orthogonality condition but few of them can result in an accurate answer as a corollary of a right decision of choosing appropriate functions. It is conceivable that finding suitable function in WPCs with low volume fraction of fiber, is not a major problem. In these amount of volume fractions of fiber, even selecting isotropic distribution of fibers in matrix, might result in good prediction, but in higher volume of fractions, like more than 40% of wood, the issue is completely different. As the volume fraction of fiber elevates, discrepancy between experimental and predictions answers ascends. Most of FEA methods like Random Sequential Adsorption and Monte Carlo codes fail to have an accurate prediction in such high volume fractions. Therefore, finding a method to compensate this lacuna is in a great interest.
Pineapple leaf fibre (PLF) from Malaysian cultivars has huge potential to be used as a reinforcing material in natural composite products or textile materials . This is because Malaysia is one of the world's major producers of pineapple, but only the fruit is used while the leaf, whose main content is fibre, is burnt or thrown away, thus causing pollution and wasting the best potential sources of natural fibre [13, 14]. Hence, the use of PLF in the natural composite materials industry can reduce environmental pollution, waste disposal problems and ecological concerns, especially in Malaysia. Mohamed et al.  studied the characterization of PLF from selected Malaysian cultivars. They found that Josapine cultivar has the best properties in terms of the quantity of fibre, fineness of fibres, thermal stability, tensile strength and modulus compared with the Sarawak and Moris cultivars, as shown in Table 1 . However, the utilization of natural fibre has a significant drawback, which is its high moisture adsorption and poor wettability with some polymer matrix . This problem can be overcome by treating these natural fibres with a suitable treatment such as alkaline treatment or heat treatment with the aim of modifying the surface of the natural fibres and improving the adhesion between the hydrophilic natural fibre and hydrophobic polymer matrix [3, 18, 31]. Siregar et al.  reported on the effects of alkaline treatments on the tensile properties of PLF reinforced high impact polystyrene composites. Their results revealed that the use of PLF with alkaline treatment improved the tensile strength and tensile modulus of the composites. The objective of the present work is to study the use of PLF from the Josapine cultivar with alkaline treatment as reinforcement to improve the mechanical properties of polypropylene composite. This research focused on the fibre extraction process and surface modification of PLF with alkaline treatment. The mechanical properties of PLF/PP composite such as tensile stress, hardness and bulk density are observed.
Other examples relate to normal or log-normal distributions. The size distributions of aerosols and clouds, and the parameters of turbulent processes are often log-normally distributed. Shoji and Kitaura (2006), for example, found that hourly, daily, and annual precipitation distributions were fitted well with log- normal distributions. The cumulative distributionfunction, D ( ) I — which indicates the probability that rainfall amount, I , will not be exceeded within period of time (hourly, daily, or annual), T — can, therefore, be given by
19. P. Stroeven, “Stereology of concrete reinforced with short steel fibres,” Heron, vol. 31(2), pp. 15-28, 1986. 20. F. Laranjeira, S. Grünewald, J. Walraven, C. Blom, C. Molins and A. Aguado, “Characterization of the orientation profile of steel fiber reinforced concrete,” Materials and structures, vol. 44(6), pp. 1093-1111, 2011.
advantages to be seen from developing alignment techniques. This finding, however, is dependent on alignment technologies meeting the development target energy consumption of 22 MJ/kg. As actual fibre alignment energy requirements may be more or less than this target, the break-even alignment energy consumption for aligned rCFRP materials are calculated to retain superior life cycle environmental performance over the best-case randomly-aligned rCFRP material. This breakeven point is found to be 95 MJ/kg and 110 MJ/kg to achieve similar life cycle PED and GWP impacts respectively. This result suggests that, should technology development objectives be achieved, then aligned rCFRP would be a promising low life cycle environmental impact material for automotive applications.
The ply stacking sequence influences directly the current density in the CFRP plies. Propagating electromagnetic waves induce electric currents in the waveguide walls . These losses are greater if the conductivity is low in the direction of the electric field, as is the case when fibres are not parallel to the field. Some of the energy from refracted electromagnetic waves penetrates through the CFRP ply and part is lost as heat. The combination of these factors explains the different attenuation constants for the different ply stacking sequences. The electromagnetic energy that flows through the walls of waveguides can be deduced from Maxwell equations. In 1884 J. H. Poynting showed that the flow of energy per unit area and per unit time equals EH sin θ . E and H are the magnitudes of the electric field intensities and θ is the angle between the vectors E and H. The flow of energy named also Poynting’s vector through the wall of the waveguides with different fibre orientations is presented in Figure 7. The values of real Pointing vector on the inner and outer surface of the waveguide (Depth location 1 and 5) and at the interface between the layers (Figure 1) are quantified to provide a depth profile of the power level in the CFRP layer in the walls of the waveguides. The energy decays exponentially as it passes through the broad and short walls of the waveguide. These results are well correlated with the values of the attenuation constant. The power level on the outside of the walls is approximately three order of magnitude lower than that on the inside wall.
These predictions can be combined with the already obtained susceptibility-induced off- resonance field, a model of eddy-current-induced off-resonance field (quadratic spatial model used for the HCP), and a model of subject motion (rigid body transform). A prediction of the distorted data can be therefore made for each 3D volume and compared with the measurements, allowing inversion of the model and estimation of the eddy-current distortions and subject motion. In an iterative process, the estimates are refined; 4–5 iterations are normally enough to achieve convergence. Using these estimates, all types of distortion are eventually corrected in a single resampling step and spline interpolation. Figure 7 illustrates a comparison of the correction of eddy-currents achieved by a typical affine transformation-based correction method, as implemented in FMRIB’s software library (FSL) (Smith et al., 2004), and the GP approach (now available in FSL 5). A qualitative comparison is shown in 7A. An axial slice was selected (inset) and a 1D profile (green line in the inset) is shown as a function of diffusion volumes (i.e. acquisition time). Head motion and eddy current-induced distortions are evident in the raw data as noisy variations of the slice boundaries (green arrows). An affine-based correction improves the situation, but clearly performs much worse than the GP approach, which achieves a better registration between volumes. A more quantitative comparison is illustrated in Figure 7B. The raw data comprised of 150 dMRI volumes acquired with a left-right (LR) PE direction, followed by the same 150 diffusion-sensitising orientations acquired with a right-left (RL) PE direction. After correcting for susceptibility-induced distortions (Andersson et al., 2003), the sum of squared differences (SSD) of signal intensities for each LR/RL pair was calculated within the brain. The plot shows the mean and standard deviation of the SSDs across all 150 pairs and for different b values. As expected, increasing the b value poses a more difficult problem. However, it is clear that in all cases the GP-based approach substantially improves the similarity between volumes, which should be identical in an artifact and noise-free scenario.
In this article, we suggest a theoretical model for anatomy and fibreorientation of the LV. The model is based on the ventricle band concept of cardiac architecture given by Torrent-Guasp . In 1972, Torrent-Guasp proposed an anatomic concept in which both right and left heart ventricles were considered segments of a single myofibre band twisted and wrapped into a double helical coil . Since that time, this concept has been a sub- ject of intense discussion. Many cardiac anatomists [14,15] consider the Torrent-Guasp hypothesis a gross simplification, and a number of imaging scientists propose a more complex organization of the LV micro-architecture . Another group of researchers has a favorable view on the ventricle band concept [17-19]. For example, an article signed by more than 20 prominent scientists  concludes that ‘models such as that of Torrent- Guasp et al., which proposes conduction along fibreorientation in a single muscular band and defies conventional concepts of activation, should be investigated’. In spite of that interest, the Torrent-Guasp model was never formalized and compared to data on measured cardiac anatomy. Note that in our view, features of the model, such as the pos- sibility of representing realistic fibre orientations by a single warped band, can be proved or disproved only by means of mathematical modelling. Regardless of the outcome, such a formulation will be useful.
C. M. Sonsino and E. Moosbrugger investigated fatigue strength behaviour of a short-glass-fibre reinforced polyamide PA66-GF35. The consideration of influencing variables like notches, fibreorientation, temperature, mean- stress and spectrum loading enable the fatigue design of high loaded plastic parts in engine compartments. A design method was developed which is based on FE calculation of the maximum local stress, the appertaining stress gradient and the highly stressed material volume.
The LPGs were clamped mid-way between two towers, one of which was mounted on a translation stage that was moved inwards to induced a bend in the optical fibre. The tags used during fabrication and markers on the fibre were used to ensure there was no unwanted twist in the fibre during the experiment. Additionally, rotation of the LPG sensor was performed on this rig by subjecting the sensor to a known curvature then rotating the sensor around its clamped axis with the flat side always pointing upwards, defining as a 0q reference the original orientation (fibre hanging downward, flat-side up), see figure 7. The broadband light source was connected to a polariser, which in turn was connected to a polarisation controller; the light from this arrangement illuminated the LPG and observations were made using an OSA.
This work begins with a discussion of the molecular properties of liquid crystals and its relevance to the form of the correlation function. From this, an expression for the free energy is developed. The qualitative features of this free energy are described in terms of the temperature and the order parameter in section 7.3. The minimisation of the free energy yields an expression for the density distribution in terms of the direct correlation function c. Thus one can obtain the expression for the pseudopotential (section 2.4) Some reasonable assumptions lead to the well-known Maier-Saupe
in close proximity, HH genes are more common. Trinklein et al. 13 greatly expanded the number of genes studied and showed that these HH pairs also show correlated expression, that many involve shared regulatory elements and that their arrangement is conserved in the mouse genome. Koyanagi et al. 14 expanded the analysis to many species, showing that this is a property specific to mammalian genomes. A study by Li et al. 15 further supported these results, showing conservation of the HH arrangement, cor- relation of expression and similarity of function. Studies confined to other organisms have also pro- vided interesting data. Cho et al. 16 and Kruglyak and Tang 17 showed that adjacent genes are co-regulated in yeast, while Williams and Bowles 18 showed the same in Arabidopsis thaliana, with HH genes showing higher correlations but longer average distances than tail to tail (TT) genes. Similarly, Roy et al. 19 showed clustering of co-expressed genes in Caenorhabditis elegans. Finally, Fukuoka et al. 20 compared gene dis- tance and co-expression in six eukaryotes and found a correlation in all six, although with significant differ- ences between them. In contrast to nearby HH genes, little research has focused on longer intergenic distance and other orientations. Some reported work on the TT-oriented gene has focused on how antisense tran- scription might play a role in their regulation. 21 – 24
The longitudinal force (radial in terms of the IVD geometry) needed to stretch a radial cut through the annulus, for two material models (Holzapfel’s model or a neo-Hookean model), is shown on Figure 2 (right). As the elongation is perpendicular to the fibre stretch, the neo- Hookean model, being isotropic, necessitates a higher force (20% greater at 20% strain).